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lenlifiauw2

Answered question

2021-11-14

Determine by inspection at least two solutions of the given first-order IVP

y^{'} = 3 y^{\frac{2}{3}}, y (0) = 0

Answer & Explanation

Julie Mathew

Beginner2021-11-15Added 15 answers

We have

y^{'} = 3 y^{\frac{2}{3}}

with initial value problen

y (0) = 0

and want to find at least 2 solutions by inspection
It is very easy to see that y=0 would be a simple solution so we need to find more
from the initial value problem we can see that the solution could have the form

y = c_{1} x^{c_{2}}

assuming

c_{1} = 1

this simplifies to

y = c_{1} x^{c_{2}}

if we also taken into account the fact that if we derive this equation we should have

y^{'} = 3 y^{\frac{2}{3}}

it is easy to see that a second solution are is

y = x^{3}

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